1. Technical Field
This invention relates to the active control of noise in an acoustic system and, in particular, to the identification of a mathematical model of the acoustic system.
2. Discussion
A review of active control systems for the active control of sound is provided in the text xe2x80x9cActive Control of Soundxe2x80x9d, by P. A. Nelson and S .J. Elliott, Academic Press, London. Most of the control systems used for active control are adaptive systems wherein the controller characteristic or output is adjusted in response to measurements of the residual disturbance or noise. If these adjustments are to improve the performance of the system, then it is necessary to know how the system will respond to any changes. This invention relates to methods for obtaining this knowledge through measurements.
Usually the active noise control system is characterized by the system impulse response, which is the time response, at a particular controller input, due to impulse at a particular controller output. This response depends upon the input and output processes of the system, such as actuator response, sensor response, smoothing and anti-aliasing filter responses, among other responses. For multi-channel systems, a matrix of impulse responses is required, one for each input/output pair. For a sampled data representation, the impulse between the jth output and the ith input at the nth sample will be denoted by aij(n).
Equivalently, the system can be characterized by a matrix of transfer functions, which correspond to the Fourier transforms of the impulse responses. These are defined for the kth frequency by             A      ij        ⁡          (      k      )        =            ∑              n        =        0                    N        -        1              ⁢                            a          ij                ⁡                  (          n          )                    ⁢              exp        (                  2          ⁢          ⅈ          ⁢                      xe2x80x83                    ⁢          kn          ⁢                      xe2x80x83                    ⁢          π          ⁢                      /                    ⁢          NT                )            
where N is an integer, the kth frequency is (kINT) and T is the sampling period in seconds.
The objective of system response identification is to find a mathematical model for the acoustic response of the system. The most common technique for system response identification is to send a random test signal from the controller output, and measure a response signal at the controller input. The response signal is correlated with the random test signal so as to reduce the effects of noise from other sources.
For many stochastic signals, the correlation can be estimated as a time average of products of the signals. For uncorrelated signals, the time-averaged power of the noise component will decrease in proportion to the averaging time. For example, if a test signal s(n) is used at time sample n to excite a system, the measured response y(n) will have two components. A first component r(n), which is the response to the test signal, and a second component d(n) which is due to ambient noise. The correlation, at a lag of m samples, between the measured response y(n) and the test signal s(n) is estimated by the time average over N samples, namely             φ      sy        ⁡          (              m        ,        N            )        =            1      N        ⁢                  ∑                  n          =          1                N            ⁢                        s          ⁡                      (                          n              -              m                        )                          ⁢                  y          ⁡                      (            n            )                              
where y(n)=r(n)+d(n).
The expected value of this correlation can be written as                               ⟨                                    φ              sy                        ⁡                          (                              m                ,                N                            )                                ⟩                =                  xe2x80x83                ⁢                              1            N                    ⁢                                    ∑                              n                =                1                            N                        ⁢                          ⟨                                                s                  ⁡                                      (                                          n                      -                      m                                        )                                                  ⁢                                  y                  ⁡                                      (                    n                    )                                                              ⟩                                                              =                  xe2x80x83                ⁢                              1            N                    ⁢                      ⟨                                          ∑                                  n                  =                  1                                N                            ⁢                              {                                                                            s                      ⁡                                              (                                                  n                          -                          m                                                )                                                              ⁢                                          r                      ⁡                                              (                        n                        )                                                                              +                                                            s                      ⁡                                              (                                                  n                          -                          m                                                )                                                              ⁢                                          d                      ⁡                                              (                        n                        )                                                                                            }                                      ⟩                                                  =                  xe2x80x83                ⁢                                            φ              sr                        ⁡                          (              m              )                                +                                    1              N                        ⁢                          φ              ss                              1                /                2                                      ⁢                          φ              dd                              1                /                2                                                        
The first term on the right hand side,                     φ        sr            ⁡              (        m        )              =          ⟨                        1          N                ⁢                              ∑                          n              =              1                        N                    ⁢                                    s              ⁡                              (                                  n                  -                  m                                )                                      ⁢                          r              ⁡                              (                n                )                                                        ⟩        ,
is the expected value of the time-averaged product of the test signal with the response to the test signal. The second term on the right hand side,                     1        N            ⁢              φ        ss                  1          /          2                    ⁢              φ        dd                  1          /          2                      =          ⟨                        1          N                ⁢                              ∑                          n              =              1                        N                    ⁢                                    s              ⁡                              (                                  n                  -                  m                                )                                      ⁢                          d              ⁡                              (                n                )                                                        ⟩        ,
is the expected value of the time-averaged product of the test signal with the noise.
The system impulse response coefficient a(m) at lag m can be estimated as             a      ^        ⁡          (      m      )        =                              φ          sy                ⁡                  (                      m            ,            N                    )                            φ        ss              .  
The expected value of xc3xa2(m) is       ⟨                  a        ^            ⁡              (        m        )              ⟩    =                    ⟨                              φ            sy                    ⁡                      (                          m              ,              N                        )                          ⟩                    φ        ss              =                                        φ            sr                    ⁡                      (            m            )                                    φ          ss                    +                        1          N                ⁢                                            φ              dd                              1                /                2                                                    φ              ss                              1                /                2                                              .                    
The first term on the right hand side is the true value for the impulse response coefficient, the second term is an error term. Clearly the error term can be reduced either by increasing the number of samples N over which the measurement is made, or by increasing the amplitude xcfx86ss of the test signal relative to the amplitude xcfx86dd of the noise.
To obtain an accurate estimate of the system response model in a short amount of time, it is therefore necessary to use a high-level or high amplitude test signal. However, this technique is in conflict to the requirement that the sound produced by the test signal must be quiet enough that it is not objectionable, since the primary purpose of an active control system is usually to reduce noise.
Prior schemes, such as those disclosed by the current inventor in U.S. Pat. No. 5,553,153, which is incorporated by reference herein, have sought to fix the accuracy of the system response model by adjusting the spectrum of the test signal so that the ratio of the test signal response to external noise is the same at each frequency. However, the prior art does not address the problem of how to maximize the accuracy or minimize the estimation time. The problem of subjective assessment of the system is also not addressed in the prior art. Moreover, in an ideal system the sound produced by the test signal should be inaudible. In the prior systems, the test signal is clearly audible, which is unacceptable in many applications.
Therefore, a need currently exists for a technique for system response identification that maximizes the accuracy of the estimated system response model and minimizes the time taken to obtain or update the estimate. There is also a need for a technique for system response identification that uses a substantially inaudible test signal. This technique for system response identification may utilize a variety of models, including transfer function models and impulse response models.
The present invention is a system and method for identifying a mathematical model of an acoustic system in the presence of noise. The system comprises a sensor, which produces a sensed signal in response to the noise at one location within the acoustic system, an acoustic actuator for producing controlled sounds within the acoustic system, and a signal processing module. The frequency spectral content of the noise is measured from the sensed signal, and a psycho-acoustical model is used to calculate a spectral masking threshold, below which added noise is substantially inaudible. The spectral masking threshold, together with a prior estimate of the transfer function between the input to the acoustic actuator and the sensed signal, is used to calculate a desired test signal spectrum. A signal generator is used to generate a spectrally shaped, random test signal with the desired spectrum. This test signal is supplied to the acoustic actuator, thereby producing a controlled sound within the acoustic system. The spectrally shaped test signal is also used as an input to an acoustic system model of the acoustic system, which includes the acoustic actuator and sensor and any associated signal conditioning devices.
The parameters of the acoustic system model are adjusted using a correlation algorithm according to the difference between the output from the acoustic system model and the sensed signal, which is responsive to the combination of the noise and the controlled sound. The correlation algorithm is implemented by an adaptation module. The frequency spectrum of the response to the spectrally shaped test signal is at or below the masking threshold and is therefore substantially inaudible.
One object of the present invention is to provide a system and method for the identification of a mathematical model of an acoustic system using a substantially inaudible test signal.
Another object is to provide a system and method for the identification of a mathematical model of an acoustic system, which provides improved accuracy.
A further object of the present invention is to provide a system and method for the identification of a mathematical model of an acoustic system, which provides improved convergence speed.